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Dividing Fractions

Key Words:
Fraction
Division
Dividend
Divisor
Quotient
Multiplicative
inverse
Reciprocal

Learning
Objectives:
• Writing whole
numbers as
fractions with
denominators of 1
Dividing whole
numbers, mixed
numbers, and
proper fractions
• Using trial and
error to find an
unknown divisor
when the
dividend and
quotient are given
• Using trial and
error to find an
unknown dividend
when the divisor
and quotient are
given

Solving Missing Value Problems when Dividing Fractions

Student Logbook

As you work through the tutorial, complete the fol lowing questions .

1. What unit of measure is used especially to define an amount of
firewood? ______________________

2. The improper fraction 5/4 is the reciprocal of __________ .

3. What is the product of 5/4 and its multiplicative inverse ? ________________

4.Write 5 as a fraction with a denominator of 1. ________________________

5. What math statement is used to check the answer for ? __________

6. In Dijit’s problem of what is the multiplicative inverse of the
divisor? ________________________________________________________

7. __________

8. If then __________ ÷ __________ = __________ .

9. __________

10. Division is the inverse of which math ope ration ? ______________________

11. Summarize the two helpful hints suggested for dividing fractions.
a. ______________________________________________________________
______________________________________________________________
b. ______________________________________________________________
______________________________________________________________

Your Turn

1. Rewrite 17 as a fraction with a denominator of 1. ____________________

2. Find Show your work. Check your answer. __________________
________________________________________________________________
________________________________________________________________

3. Chip uses cups of water to make 5 portions of his special stew. How
many cups would he use for just one portion? ________________________

4. Dijit changes the stew recipe so that he uses cups of water to make
6 portions. How many cups of water does the changed recipe use per
single portion? __________________________________________________

5. What is the missing divisor in the following equation?
8 ÷ __________ = 5

6. What is the missing dividend in the following equation?
__________

7. What is the missing divisor in the following equation?
9 ÷ __________ = 4

8. Show how you can check your work in Question 7. __________________
________________________________________________________________
________________________________________________________________

Unit Review

Estimating Quotients of Fractions

1. Rewrite 4/5 as an equivalent fraction with a denominator of 10.
________________________________________________________________

2. Round the following fractions to the nearest whole numbers.

3. To prepare condensed soup for a crowd, Sophie mixes 2/3 cup of milk with
each can of condensed soup. She uses a total of 4 cups of milk. How
many cans of soup will she need? Show your work.
________________________________________________________________
________________________________________________________________
________________________________________________________________

Using Multiplicative Inverses

4. Rewrite the following mixed numbers as improper fractions.

5. Using multiplicative inverses, rewrite these division problems as
multiplication problems. If necessary, convert mixed numbers to improper
fractions.

6. To make a fruit punch, Dijit needs to mix 1/2 cup of the fruit punch powder
with 1 quart of water. The fruit punch container holds 4 cups of powder.
How many quarts of water does Dijit need to mix with one whole
container of the powder? ________________________________________

Solving Missing Value Problems when Dividing Fractions

7. For a summer job, you mow lawns. Your lawn mower uses 2/3 gallon of
fuel an hour. If you used 6 gallons of fuel one day, how many hours did
you spend mowing grass that day? Show your steps and check your
answer. ________________________________________________________

8. Sophie spends hours on a shopping trip for her clients. She spends
the same amount of time, hours, at each store she visits. How many
stores does she visit? Show the steps you use to solve the problem.
________________________________________________________________

Putting It All Together

9. The net weight of bolts in a keg is pounds. The weight of one bolt
is ounces. How many bolts are there in the keg? (Remember to
convert pounds to ounces.) ________________________________________

10. Chip builds a fence that is yards long, with a post at each end. He
has a total of 14 fence posts, including the two at each end. How far
apart should he place his posts? Make a drawing and show your work.
________________________________________________________________

Unit Assessment

1. Your friend wants your help to solve the problem Write words
and steps that explain how to find this quotient. ______________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________

2. a. Place a point on the number line to show to the nearest whole
number.
b. Is closer to 2 or 3? ______________________

3.Write a problem with a divisor that is a whole number, a dividend that is
a mixed number, and a quotient that is a proper fraction in lowest terms.
________________________________________________________________

4. Find the multiplicative inverse of ________________________________

5. Can the reciprocal of a proper fraction always be written as a mixed
number? __________ Explain. ____________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________

6. Chip has 3/4 of a pizza that he wants to divide equally between himself
and two of his friends. What fraction of the pizza will Chip get?
Show your work. ________________________________________________
__________________________________________________________________

7. Sophie is de signing a decorator item using colored yarn. She needs 35
pieces of yarn that are 1/4 yard each to complete the project. She has
yards of yarn. Will Sophie have enough yarn to complete her design?
__________ Explain your answer. __________________________________
__________________________________________________________________
__________________________________________________________________

8.Will the reciprocal of a whole number (other than 1) be a proper fraction or
an improper fraction? Explain. ____________________________________
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________

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